Development of averaged solid–fluid potential energies for layers and solids of various geometries and dimensionality

The solid–fluid (SF) interaction energy describes the affinity between one adsorbate molecule and a solid. Its quantification is an essential input for the simulation of the adsorption isotherm, the isosteric heat and details of the microscopic structure of the adsorbate. A good approximation to the SF energy can be obtained by direct summation of all effective pairwise interaction energies (LJ plus electrostatic) between an adsorbate molecule and all the atoms in the solid. To repeat this summation for each new configuration in a simulation is very time-consuming. One resolution is to construct database tables of the solid–fluid potentials, which leads to massive databases if the grid separation used is very small. For solids that have simple geometries an alternative is to determine the approximate solid–fluid potential by ignoring the discrete atomic structure of the solid. This level of approximation is adequate for many simulations of engineering interest where fine details, for example in the first adsorbate layer, are not necessary. In this paper, we report comprehensive derivations of solid–fluid potentials for a wide range of solids, in layered structures with constant surface atom density or solid structures with constant atom density, and various curvatures and dimensions. These solids are common in engineering applications and the derived analytical solutions will be of value to scientists and engineers. We take a finite solid as an example of the application of the SF potential equations developed in this paper, and show the spatial variation of the solid–fluid potential energy in the neighbourhood of the edges of the solid, which is found to be remarkably different from the usual 1D potential energy equation commonly used in the adsorption literature.